Attractor invariants for the local Hirzebruch-surface quiver

Let $Q$ be the quiver for the local Hirzebruch surface $K_{\mathbb{F}_0}$, let $e_i$ be its vertex dimension vectors, and let $\mathrm{d}=(1,1,1,1)$ be the dimension vector of a single D0-brane. Local Hirzebruch-surface attractor conjecture. For every vertex $i$, $\Omega_*(e_i)=1$, and for every $n\geq1$, $\Omega_*(n\mathrm{d})=-y^{-1}(y^2+1)^2$; all other attractor invariants vanish. The formula was verified in small degrees and is compatible with the motive of $K_{\mathbb{F}_0}$; the source also records the corresponding single-centered relation as a consequence supported by earlier conjectural work.